Scattering of time-harmonic electromagnetic plane waves by perfectly conducting diffraction gratings
Scattering of time-harmonic electromagnetic plane waves by perfectly conducting diffraction gratings
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DOI：
10.1093/imamat/hxt054
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发表时间：
2012-09
影响因子：
1.2
通讯作者：
G. Hu;A. Rathsfeld
中科院分区：
文献类型：
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作者：
G. Hu;A. Rathsfeld
考虑时间简谐电磁平面波在R3中双周期表面的散射，假设表面上方的介质是均匀各向同性的，具有常数的介电系数，而下方的材料是完全导电的。本文讨论了任意频率下拟周期解的存在性。基于Nitsche的Morar技术建立的等价变分公式，我们证明了包括平面波在内的一大类入射波的解的存在性。唯一的假设是，光栅轮廓是一个Lipschitz双周期曲面。请注意，本文的可解性结果涵盖了允许瑞利频率的共振情况。最后，给出了经典光栅在共振情况下和TE、TM偏振情况下的非唯一性例子。
Consider the scattering of time-harmonic electromagnetic plane waves by a doubly periodic surface in R 3. The medium above the surface is supposed to be homogeneous and isotropic with a constant dielectric coefficient, while the material below is perfectly conducting. This paper is concerned with the existence of quasiperiodic solutions for any frequency. Based on an equivalent variational formulation established by the mortar technique of Nitsche, we verify the existence of solutions for a broad class of incident waves including plane waves. The only assumption is that the grating profile is a Lipschitz biperiodic surface. Note that the solvability result of the present paper covers the resonance case where Rayleigh frequencies are allowed. Finally, non-uniqueness examples are presented in the resonance case and in the case of TE or TM polarization for classical gratings.